The Connacht side looked to be heading for their fifth straight loss, after Eric Lavine returned to haunt his old club with a goal early in the opening half.
Lavine wrong sighted Michael Quirke before drilling a superb low shot across Eddie Hickey into the bottom corner of the keeper's net.
However, Galway were back in the game on the half-hour mark. Paul McNally felled Ollie Keogh in a packed penalty area and Clery, who passed a late fitness test, slotted home the equalizer from the spot.